ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 52C25 Alexandrov, Victor, Sobolev Institute of Mathematics, Novosibirsk, Russia Sufficient conditions for the extendibility of an N-th order flex of polyhedra A very long-standing (and still open) problem is to prove that a smooth compact surface in the Euclidean 3-space is rigid. Classical attempts to solve this problem were based on the notion of an infinitesimal flex. Since a counterexample was constructed by R. Connelly in the class of polyhedral surfaces, particular attention was given to studying infinitesimal flexes of polyhedra. We give a new approach to describing a high order flex of polyhedra. The main results provide some sufficient conditions under which an infinitesimal flex of a polyhedron can be extended to an authentic flex. We discuss also results of computer experiments demonstrating that one set of our sufficient conditions is fulfilled for Bricard octahedra.